This paper proposes a three-level hierarchical mathematical model for intel
ligent and complex systems. Motivation, background, rationale, interpretati
ons and potential applications are presented. Different visions from differ
ent schools of thought in various academic disciplines are illustrated in a
block; diagram. The concept of "soft-modeling", representing a dramatic de
parture from conventional mathematical modeling, is also proposed. The char
acteristics, approach, types of mathematics used and the interpretations th
at will eventually lead to engineering realization and commercialization ar
e also presented. (C) 2000 Elsevier Science Inc. All rights reserved.